A193354 Triangle: T(n,k) = (-1)^(n-i) * r16(n-i) * 2^(3*b(i)) * sigma_3(O(i)), for k=1 to n, for n>=1 (see comments for terms used).

1, -32, 8, 480, -256, 28, -4480, 3840, -896, 64, 29152, -35840, 13440, -2048, 126, -140736, 233216, -125440, 30720, -4032, 224, 525952, -1125888, 816256, -286720, 60480, -7168, 344, -1580800, 4207616, -3940608, 1865728, -564480, 107520, -11008, 512

Offset

1,2

Comments

Functions used in name: r16(n) is A000152(n), O(n) is A000265(n), b(n) is A007814(n).

For n>=1, Sum_{k=1, n} a(k) = A000594(n).

Links

Table of n, a(n) for n=1..36.

John A. Ewell, A formula for Ramanujan's tau function, Proc. Amer. Math. Soc. 91 (1984), 37-40

Example

Triangle starts:
1: 1
2: -32, 8
3: 480, -256, 28
4: -4480, 3840, -896, 64
5: 29152, -35840, 13440, -2048, 126

Crossrefs

Cf. A000152, A000265, A000594, A007814, A001158, A051000.

Sequence in context: A120315 A119362 A070630 * A070622 A213656 A302216

Adjacent sequences: A193351 A193352 A193353 * A193355 A193356 A193357

Keyword

sign,tabl

Author

Michel Marcus, Dec 20 2012

Status

approved